NOTES
300
tions prepared from three different commercial preparations of urea at several concentrations differed by only *0.0002. Thus, only the more extensive data obtained with the Mallinckrodt preparation are summarized in Table I. The refractive indices of urea solutions are extensively used for the reduction of the optical rotatory power of macromolecules in urea solutions to values they would have under vacuum by means of the Lorenz-Lorents correction.lgb Comparing our refraction data at the sodium D doublet to the older and widely used data,lSo major discrepancies increasing with urea concentration are seen (compare columns 1 and 5 of Table I). At 8.00 M urea the older value of the refractive index is +0.0082 higher than the value obtained in this study, a difference well outside our maximum over-all experimental error of =k0.0002. We are unable to ascribe this deviation to small errors in technique or to extremes in ambient temperature and pressure which usually give rise to differences less than a few units in the fifth decimal place.20 Moreover, Foss, Kang, and Schellman recently obtained data for 8.00 M urea at 20’ as a function of wave length,ledand a comparison of their data with ours a t 436 and 546 mp and an extrapolation of their data to 589 mp reveal positive differences ascribable to minor experimental variations of two units or less in the fourth decimal place; therefore, their data are consistent with the present report. I n view of the refractive index and viscosity data reported in this communication, it seems, therefore, that urea solutions do not undergo a detectable transition in structure a t some critical concentration or concentration range of urea. This is not entirely surprising in view of Gucker, Gage, and Moser’s elegant study on the densities of aqueous urea solutions which showed that the apparent molal volume of urea is a linear function of the first power of the volume concentration up to 4 M , suggesting that urea is very nearly a perfect solute and does not exhibit the large electrostriction of electrolytes and polar nonelectrolyte~.~
Acknowledgment. Support by a grant from the National Institute of General Medical Sciences, U. S. Public Health Service (GM-11345-02), to Julius A. Gordon is acknowledged. ~~~
~
(19) (a) G.Fasman in “Methods in Emymology,” Vol. VI, Academic Press Inc., New York, N. Y.,1963, P. 952; (b) ibid., P. 930; (0) ibid., Table VI; (d) ibid., p. 957. (20) See ref. 13,p. 1141.
The Journal of Physical Chemistry
The Principle of Microscopic Reversibility by Robert L. Burwell, Jr., and Ralph G. Pearson Department of Chemistry, Northwestern University, Evanaton, Illinois (Received August 9, 1966)
The principle of microscopic reversibility, p.m.r., is often invoked to exclude certain postulated reaction mechanisms. This principle states’ that any molecular process and its reverse occur with equal rates at equilibrium. In mechanistic terms it states that, if a certain series of steps constitutes the mechanism of a forward reaction, the mechanism of the reverse reaction (under the same conditions) is given by the same steps traversed backwards.2 Thus, it is certainly valid to exclude all other mechanisms in any case when the reverse mechanism is known. However, the p.m.r. is often used as a basis for exclusion where neither mechanism is known beforehand. The exclusion is usually due to a certain lack of symmetry in the forward and reverse direction^.^ The argument is most easily seen for the case of isotopeexchange reactions, where, if kinetic isotope effects are ignored, the mechanism must be precisely the same in both directions, The purpose of this note is to point out the exact nature of the application of the p.m.r. to such isotope-exchange reactions. This can be simply done by drawing conventional free energy profiles along reaction coordinates. If the exchange reaction proceeds by but one path, then p.m.r. does indeed require a symmetric free energy profile with respect to the reaction path. If the number of intermediates formed is even, including zero, the two isotopic atoms entering and leaving become equivalent in the central transition state; if odd, in the central intermediate. This is illustrated in Figure l a ~ between CHJ3r and *Br- (zero interfor an S Nreaction mediates) and in Figure l b for an SN1 reaction between &butyl bromide and *Br- (one intermediate, (CH3)aCf Br*Br-). Two or more atoms are equivalent if, within an appropriate time period, the environments seen from the nuclei of the two or more atoms are identical or are mirror images of each other. The p.m.r. does not permit a one-path mechanism
+
+
(1) R. C. Tolman, Phys. Rev., 23, 699 (1924); “The Principles of Statistical Mechanics,” Oxford University Press, London, 1938, pp. 163, 165. (2) A. A. Frost and R. G. Pearson, “Kinetics and Mechanism,” John Wiley and Sons, Inc., New York, N. Y.,1961,pp. 211-213. (3) For a recent example see 8. L. Johnson, J. Am. Chem. SOC.,8 6 , 3819 (1964). The author rejects nonsymmetric reaction paths by incorrect application of the p.m.r.
NOTES
301
The example shown in Figure Id wm originally suggested4 as a mechanism which might be applied to an exchange reaction such as Pt(NH$Sr+-*Br-. The steps would be
S r.c.
*Br
r.C.
+ *Br--
(b)
fast
A
Pt
Pt
\\,
I
- \I/ / NH3
/// 3"
NH3'
S
+
+
+
+
which is not symmetric about the midpoint of the free energy profile. However, it does permit such a process as a two-path mechanism in which the second path is that obtained by reflecting the first in a plane at the midpoint. As shown in Figure ICand d, the sum of the two paths is symmetric, but the isotopic atoms never become equivalent. Such two-path mechanisms will usually be associative rather than dissociative in nature. Since an isotope-exchange reaction occurs under equilibrium conditions, if isotope effects are not considered, the p.m.r. also requires that exactly 50% of the exchange occurs by the solidline path and 50% of the exchange occurs by the dottedline path of Figure ICand d. That is, the rates are exactly the same for each mechanism since both must be in equilibrium. Reactions of the type of Figure ICmust be common and, in particular, will involve associative exchange processes in which the isotopic atoms cannot become equivalent because there are one or more asymmetric centers elsewhere in the molecule. Here the isotopic atoms are not equivalent because the two environments which are seen are epimeric. An example would be oxygen isotope exchange between 3-methyl-2pentanone and water via the ketone hydrate. Notice that there are two epimeric transition states of equal energy, each reached by its own path.
NH3'l
Pt
I
S
S
*Br
Figure 1. Free energy us. reaction coordinate for the exchange *Br-; reactions: (a) CH3Br *Br-; (b) t-(CH&CBr (c) CH&H&H(CHs)COCHg Hz*O; (d) Pt(NH&Br+ *Br-.
(2)
NH3
slow
A
Pt
rx.
+ Br-
*Br
*Br
AG
(1)
S
S
*"
+s
Pt
Pt
(3)
NH3( \Br*
s
S
There are good reasons for discarding this mechanism in favor of a simpler one in which the five-coordinated intermediate is more symmetrical.6 The im*Br
Pt '3"
\
Br
portant point is that the mechanism shown in reactions 1, 2, and 3 is not excluded by any fundamental principle such as that of microscopic reversibility. It and its reverse, reactions 3, 2, and 1, taken together do not violate any known laws and comprise a possible multipath mechanism. In mechanism of the type in Figure Id, the positions of the isotopic a t o m are structurally isomeric rather than epimeric. Because of this, there is no possibility of a system on the solid-line path crossing over to the dotted-line path at the midpoint where (4) D. Banerjea, F. Basolo, and R. G. Pearson, J. Am. Chem. Soc., 79, 4055 (1957). (5) This is the Chatt-Orgel mechanism. See F. Basolo and R. G. Pearson, Prop. Inorg. Chem., 4, 381 (1962).
Volume 70, Number 1 January 1966
NOTES
302
states of oxygen, Oz(alA) and 02(b1Z).384 Both of these electronically excited states are formed in the upper and lower atmosphere by the direct absorption of sunlight.6 Their importance to atmospheric photochemistry depends on their collisional deactivation rate, as pointed out by Leighton.E The rate of collisional deactivation of 02(b1Z) by N2 has been measured recently.’ This note is concerned with. deactivation of 02(a1A).
*I
*
*I
*I
*
*
Figure 2. Example of the mechanism of Figure Id.
they apparently met. Thus, the reaction coordinates for the two paths, while otherwise identical, are located in different parts of coordinate space. This is also true in Figure IC. As far as we know, no one has postulated such a multipath reaction for any homogeneous isotopic exchange reaction. More commonly, some more symmetric reaction path will be of lower energy. However, multipath processes have been proposed in heterogeneous exchange and racemization reactions.6 The presence of a surface may often prevent the f o m tion of symmetrical intermediates. Figure 2 shows the details of a two-path mechanism for deuterium exchange in bemene on a metal surface in which hydrogen is added from one side of the ring and removed from the other side. The application of the above ideas to substitution reactions which are not isotopic exchanges is straightforward. We conclude that any conceivable reaction mechanism which consists of a limited combination of allowed elementary steps will occur though its rate may be too small to have any experimental consequences. By allowed we mean not forbidden by energy requirements or selection d e s . (6) R. L. Burwell, Jr., and W. 5. Briggs, J . Am. Chem. Soc., 74,5101 (1952); J. R. Anderson, Rev. Pure Appl. Chem., 7 , 186 (1957); F. G. Gault, J. J. Rooney, and C. Kembd, J . Catalysis, 1, 255 (1962).
The Decay of 02(a1A) in Flow Experiments’
by Arthur M. Winer2 and Kyle D. Bayes Departmen$ of Chenaistry, University of California, Lo8 Angeles, Califmnia 90094 (Received Avgust 6,1966)
Recently, methods have been developed for generating large quantities of the two metastable singlet The J ~ u ofdPhg&
Chentbtry
Experimental Section The singlet oxygen was generated in a system similar to that of Elias, et aL3 Tank oxygen (>99.9%, Liquid Carbonic) was admitted to a flow system at a few torr pressure, passed over mercury at about 23”, and then through a discharge in a cylindrical microwave cavity (maintained by 40 to 60 w. at 2450 Mc.). The mercury vapor formed a brown coating of mercuric oxide downstream from the discharge, which efficiently removes oxygen atoms and apparently enhances the alA state concentration.8 When the atoms were not being completely removed, the air glow, due to the 0 plus NO reaction, could be easily observed in the darkened room. Checks were made from time to time to confirm the absence of the air glow. Then the gas passed through a trap containing water at about -40”. This introduced sufficient gaseous HzO to deactivate any blZ state molecules before the decay experiments.@ The gas thus contained only diatomic oxygen in its ground and a’A states, and traces of Hg, H20, and NO (from the original nitrogen impurity in the oxygen). The gas then entered a cylindrical Pyrex tube, 20.0 mm. in i.d. and 2 m. long. Four identical inlet stations were built into the tube, each consisting of three nozzles symmetrically placed in a plane perpendicular to the axis of the tube. The nozzles projected 3 mm. into the gas stream. The first station was 36 cm. from (1) Contribution No. 1847 from the Department of Chemistry, University of California, Los Angeles, Calif. (2) National Science Foundation Undergraduate Research Participant. (3) L. Eli=, E. A. Ogryzlo, and H. I. SchifF, Can. J . Chem., 37, 1680 (1959). (4) S. J. Arnold, E. A. Ogryzlo, and H. Witze, J . Chem. Phys., 40, 1769 (1964). (6) A. Valiance-JoneaTand A. W. Harrison, J . Atmospheric Terrest. Phys., 13, 46 (1958). (6) P. A. Leighton, “Photochemistry of Air Pollution,” Academic Preas, New York, N. Y.,1961. (7) R. A. Young and G. Black, J . Chem. Phys., 42, 3740 (1965). (8)R. E.Marsh, S. G. Furnival, and H. I. SOW,Preprint of Papers, Symposium on Chemiluminescence, Durham, N. C., 1965, p. 51. (9) L. W. Bader and E. A. Ogryzlo, Discussions Faraday SOC.,37, 461 (1964).
